# Perform a one-sided hypothesis t-test

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In an attempt to determine whether or not special training increases the speed with which assembly line workers can do an assembly job at AMTEL Inc., 25 workers are timed performing the task. Then, they are given a special training course designed to increases their assembly efficiency. At the end of the course, they are timed doing the same task. The differences between the first and the second time are recorded for each of the 25 assembly line workers. The mean improvement for the 25 workers was found to be 2.5 minutes and the sample standard deviation was 4 minutes.

Let variable X represents the improvement in time for each assembly line worker. Let ? represents the average improvement in time for the population. Has the training improved the time required on the job? Please test the hypothesis use ?=0.05 as the level of significance

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##### Solution Summary

The solution consists of a standard five-step one-sided hypothesis t-test for the population mean.

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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